$A$ massless spring gets elongated by an amount $x_1$ under a tension of $5 \ N$. Its elongation is $x_2$ under a tension of $7 \ N$. For an elongation of $(5x_1 - 2x_2)$,the tension in the spring will be: (in $N$)

The length of a spring is $\alpha$ when a force of $4\,N$ is applied on it and the length is $\beta$ when $5\,N$ force is applied. Then the length of the spring when $9\,N$ force is applied is

$A$ spring whose unstretched length is $\ell$ has a force constant $k$. The spring is cut into two pieces of unstretched lengths $\ell_1$ and $\ell_2$ where $\ell_1 = n\ell_2$ and $n$ is an integer. The ratio $k_1/k_2$ of the corresponding force constants $k_1$ and $k_2$ will be:

Two massless springs of spring constants $K_1$ and $K_2$ are connected in series, suspended vertically, and a mass is attached to the free end. If $x_1$ and $x_2$ are their respective extensions and $F$ is the stretching force, what is the total extension produced?

$A$ bead of mass $m = 100 \,g$ is attached to one end of a spring of natural length $L$ and spring constant $k = \frac{(\sqrt{3}+1) mg}{L}$. The other end of the spring is fixed at point $A$ on a smooth vertical ring of radius $R$. The bead is at point $B$ such that the spring makes an angle of $30^{\circ}$ with the horizontal diameter. The normal reaction at $B$ just after it is released to move is (take $g = 9.8 \,ms^{-2}$): (in $\,N$)

Two blocks with masses $100 \text{ g}$ and $200 \text{ g}$ are attached to the ends of springs $A$ and $B$ as shown in the figure. The energy stored in spring $A$ is $E$. The energy stored in spring $B$, when the spring constants $k_{A}$ and $k_{B}$ of springs $A$ and $B$ respectively satisfy the relation $4k_{A} = 3k_{B}$, is: